Question

If a soap film of refractive index 1.33, surrounded by air, is illuminated by a red (633 nm) and a green (515 nm) light, find the minimum film thickness at which the reflected light will appear red. Repeat to find the thickness at which is will appear green.

Answer 1

The minimum thickness of a soap film for red light (633 nm) to appear is approximately 238 nm, and for green light (515 nm) it is approximately 194 nm, based on constructive interference in thin films.

Step-by-step explanation:

To find the minimum thickness of a soap film that makes the reflected light appear red for a wavelength of 633 nm, we use the constructive interference condition for thin films. When light reflects off the top surface of a film, it undergoes a phase shift of π, while the light reflecting off the bottom surface doesn't if the medium below has a higher refractive index.

Therefore, for constructive interference, the path length difference should be an integer multiple of the wavelength in the medium, λ/n.

The formula for minimum thickness is t = (λ/2n) for the first order where m=0

(as m=0.5 would result in destructive interference).

The minimum thickness for red light to appear is t = 633 nm / (2 * 1.33) ≈ 238 nm.

Similarly, for green light with a wavelength of 515 nm, t = 515 nm / (2 * 1.33) ≈ 194 nm.